Planck distribtion

I cant find the proof of "the ratio of the number of oscillators in their (n+1) )th quantum state of excitation to the number in nth quantum state is:
k is boltzman costant
N_(n+1)/N_(n)=exp(-hω/2π(kT)"2. Relevant equations

So, the Boltzmann factor can be proved using Entropy of a reservoir and a particle in state i. The gist of it is, if you change the state of the particle, you change the energy of the particle and the entropy (multiplicities) of the reservoir. If you use some entropy and multiplicity relations, you can get the Boltzmann factor.